Finite-State Methods for Sub-Atomic Semantics

ESSLLI 2015, Barcelona (2nd week, Language & Computation)

Tim Fernando

Abstract

Subatomic Semantics is according to Parsons 1990

   "the study of those 'formulas of English' that are treated as 
    atomic formulas in most logical investigations of English" 

including tense and aspect, and predication/modification.
Implicit in the idea of subatomic semantics is non-atomicity, or put more 
positively, open-endedness. 
One form of open-endedness is variable adicity, the raison d'etre of events in 
Davidson 1967.
A second form of open-endedness arises from the choice of temporal propositions,
changes in which determine a notion of time. 
We analyze open-endedness uniformly through variations in bounded granularities
shaping models within institutions in the sense of Goguen and Burstall 1992.
Institutions are built around finite models of two kinds

   (i) strings, as in the Buechi-Elgot-Trakhtenbrot representation of regular
       languages in Monadic Second-Order Logic with successor, and 

  (ii) deterministic automata, reduced under Myhill-Nerode to languages with 
       transitions given by Brzozowski derivatives.

The strings in (i) are used as timelines (approximating Priorean models), and 
the automata in (ii) as frames or records encoding a causal realm and/or 
linguistic resources.
Central to Parsons' understanding of subatomic semantics is

   "the Panini-Ramsey-Davidson hypothesis that English sentences of
    the simplest sort contain some underlying reference to
    (quantification over) events or states."

An addendum to the Panini-Ramsey-Davidson hypothesis is finite approximability: 

  events are approximable at bounded granularities as runs of finite automata.

The aim of the course is to show that these approximations are interesting,
and that finite automata can, to a non-trivial extent, serve as the causal 
structures central, according to Steedman, to temporality in natural language.

References

patches from which are stitched together by papers of the lecturer below.

Lecture 1. Introduction: the Big Picture & an overview (slides)

Prior and temporal sequences for natural language, Synthese, to appear (special issue on Arthur Prior centenary)
Partitions representing change homogeneously, A festschrift for Jeroen Groenendijk, Martin Stokhof & Frank Veltman, 2013 (pages 91--95)

Key phrases: McTaggart's dictum, temporal proposition (fluent), homogeneity, Dowty's Aspect hypothesis, segmentation, Dedekind cut

Lecture 2. MSO/strings, compression & regular relations (slides)

Constructing situations and time, J Philosophical Logic 40: 371--396, 2011
Regular relations for temporal propositions, Natural Language Engineering 17(2): 163--184, 2011
On regular languages over power sets, Journal of Language Modelling, to appear (FSMNLP/IWPT 2013 special issue)

Key phrases: Carnap-Montague intensions, Buechi-Elgot-Trakhtenbrot theorem, Allen interval relations, Russell-Wiener-Kamp event structures, finite-state transducers

Lecture 3. A finite-state perspective on tense & aspect (slides)

The semantics of tense and aspect: a finite-state perspective, In S. Lappin & C. Fox (eds.), The Handbook of Contemporary Semantic Theory, Second Edition, Wiley

Key phrases: telic, durative, Aktionsart, imperfective, telic, segmented, whole, incremental change, forces and inertia

Lecture 4. Frames as finite automata (slides)

Types from frames as finite automata, In Foret, Morrill, Muskens & Osswald (eds.), Preproceedings of the 20th Conference on Formal Grammar 2015, Barcelona

Key phrases: Leibniz' law, Myhill-Nerode theorem, Brzozowski derivative, Grothendieck construction, record types

Lecture 5. Conclusion: partial views & prospects (slides)

Two perspectives on change and institutions, In Joint Ontology Workshops proceedings (FOfAI), 2015, Buenos Aires

Key phrases: ontology, truthmakers, mereology, institutions (logical pluralism, heterogeneity)


Last modified: 25 August 2015